What is the integral of sec(8x)tan(8x) ?

The integral of sec(8x)tan(8x) is 1/8 sec(8x)+C

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integral of sec(8x)tan(8x)

\int sec (8 x) tan (8 x) d x

\frac{1}{8} sec (8 x) + C

Solution steps

\int sec (8 x) tan (8 x) d x

Apply u-substitution

: \int \frac{1}{8} d u

= \int \frac{1}{8} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{8} u

Substitute back

u = sec (8 x)

= \frac{1}{8} sec (8 x)

Add a constant to the solution

= \frac{1}{8} sec (8 x) + C

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\frac{d}{d x} ((x^{\frac{2}{3}}) (6 - x)^{\frac{1}{3}})

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What is the integral of sec(8x)tan(8x) ?
The integral of sec(8x)tan(8x) is 1/8 sec(8x)+C